共查询到20条相似文献,搜索用时 15 毫秒
1.
Kristine Ey 《Journal of Difference Equations and Applications》2013,19(10):953-965
We investigate a class of second-order linear difference equations by applying results of harmonic analysis on polynomial hypergroups. For the scalar case we show that the solutions are either bounded by the modulus of the initial value or are unbounded. For the Hilbert space-valued case we establish a concrete representation of the solutions whenever they are bounded and stationary. Among various examples we discuss those corresponding to Jacobi polynomials. 相似文献
2.
Mustafa Gülsu Mehmet Sezer 《Numerical Methods for Partial Differential Equations》2011,27(6):1628-1638
A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011 相似文献
3.
Jean Letessier André Ronveaux Galliano Valent 《Journal of Computational and Applied Mathematics》1996
An explicit representation of the associated Meixner polynomials (with a real association parameter γ?0) is given in terms of hypergeometric functions. This representation allows to derive the fourth-order difference equation verified by these polynomials. Appropriate limits give the fourth-order difference equation for the associated Charlier polynomials and the fourth-order differential equations for the associated Laguerre and Hermite polynomials. 相似文献
4.
Adomian polynomials: A powerful tool for iterative methods of series solution of nonlinear equations
下载免费PDF全文
![点击此处可从《Journal of Applied Analysis & Computation》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Ahmed Elsaid 《Journal of Applied Analysis & Computation》2012,2(4):381-394
In this article, we illustrate how the Adomian polynomials can be utilized with different types of iterative series solution methods for nonlinear equations. Two methods are considered here: the differential transform method that transforms a problem into a recurrence algebraic equation and the homotopy analysis method as a generalization of the methods that use inverse integral operator. The advantage of the proposed techniques is that equations with any analytic nonlinearity can be solved with less computational work due to the properties and available algorithms of the Adomian polynomials. Numerical examples of initial and boundary value problems for differential and integro-differential equations with different types of nonlinearities show good results. 相似文献
5.
本文给出了分数阶积分微分方程的一种新的解法.利用未知函数的泰功多项式展开将分数阶积分微分方程近拟转化为一个涉及未知函数及其n阶导数的线性方程组.数值例子表明该方法的有效性. 相似文献
6.
V. Laohakosol W. Rungrottheera 《Journal of Mathematical Analysis and Applications》2007,335(1):280-297
Under certain natural conditions, it is shown that exponential polynomials are the only entire function solutions of a system of two recurrent step equations consisting of one with constant coefficients and the other with exponential polynomial coefficients. 相似文献
7.
Salih Yalinba Mehmet Sezer Hüseyin Hilmi Sorkun 《Applied mathematics and computation》2009,210(2):334-349
In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed. 相似文献
8.
A. Elsaid 《Applied mathematics and computation》2012,218(12):6899-6911
A modification of the fractional differential transform method (FDTM) for solving nonlinear fractional differential equations (FDEs) is presented. In this technique, the nonlinear term is replaced by its Adomian polynomial of index k. Then the dependent variable components are replaced in the recurrence relation by their corresponding differential transform components of the same index. Thus nonlinear FDEs can be easily solved with less computational work for any analytic nonlinearity due to the properties and available algorithms of the Adomian polynomials. Numerical examples with different types of nonlinearities are solved and good results are obtained. 相似文献
9.
In this paper we provide a version of the Floquet’s theorem to be applied to any second order difference equations with quasi-periodic coefficients. To do this we extend to second order linear difference equations with quasi-periodic coefficients, the known equivalence between the Chebyshev equations and the second order linear difference equations with constant coefficients. So, any second order linear difference equations with quasi-periodic coefficients is essentially equivalent to a Chebyshev equation, whose parameter only depends on the values of the quasi-periodic coefficients and can be determined by a non-linear recurrence. Moreover, we solve this recurrence and obtaining a closed expression for this parameter. As a by-product we also obtain a Floquet’s type result; that is, the necessary and sufficient condition for the equation has quasi-periodic solutions. 相似文献
10.
A new numerical approach for the solution of nonlinear Fredholm integral equations system of second kind by using Bernstein collocation method
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
This paper presents an efficient numerical method for finding solutions of the nonlinear Fredholm integral equations system of second kind based on Bernstein polynomials basis. The numerical results obtained by the present method have been compared with those obtained by B‐spline wavelet method. This proposed method reduces the system of integral equations to a system of algebraic equations that can be solved easily any of the usual numerical methods. Numerical examples are presented to illustrate the accuracy of the method. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
12.
Mourad E.H. Ismail Plamen Simeonov 《Journal of Mathematical Analysis and Applications》2011,376(1):259-274
We study polynomials orthogonal on a uniform grid. We show that each weight function gives two potentials and each potential leads to a structure relation (lowering operator). These results are applied to derive second order difference equations satisfied by the orthogonal polynomials and nonlinear difference equations satisfied by the recursion coefficients in the three-term recurrence relations. 相似文献
13.
John T. Conway 《Integral Transforms and Special Functions》2020,31(4):253-267
ABSTRACTElementary linear first and second order differential equations can always be constructed for twice differentiable functions by explicitly including the function's derivatives in the definition of these equations. If the function also obeys a conventional differential equation, information from this equation can be introduced into the elementary equations to give blended linear equations which are here called hybrid equations. Integration theorems are derived for these hybrid equations and several universal integrals are also derived. The paper presents integrals derived with these methods for cylinder functions, associated Legendre functions, and the Gegenbauer, Chebyshev, Hermite, Jacobi and Laguerre orthogonal polynomials. All the results presented have been checked using Mathematica. 相似文献
14.
J.A. Rad S. Kazem M. Shaban K. Parand A. Yildirim 《Mathematical Methods in the Applied Sciences》2014,37(3):329-342
In this paper, we state and prove a new formula expressing explicitly the integratives of Bernstein polynomials (or B‐polynomials) of any degree and for any fractional‐order in terms of B‐polynomials themselves. We derive the transformation matrices that map the Bernstein and Legendre forms of a degree‐n polynomial on [0,1] into each other. By using their transformation matrices, we derive the operational matrices of integration and product of the Bernstein polynomials. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations. The method is applied to solve linear and nonlinear fractional differential equations. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
15.
In this paper, a new approximate method has been presented to solve the linear Volterra integral equation systems (VIEs). This method transforms the integral system into the matrix equation with the help of Taylor series. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Also, this method gives the analytic solution when the exact solutions are polynomials. So as to show this capability and robustness, some systems of VIEs are solved by the presented method in order to obtain their approximate solutions. 相似文献
16.
This article is a survey of the recent studies jointly with Lies Boelen, Christophe Smet, Walter Van Assche and Lun Zhang (KULeuven, Belgium) on semi-classical continuous and discrete orthogonal polynomials and, in particular, on the connection of their recurrence coefficients to the solutions of the Painlevé equations. After recalling some basic facts about the Painlevé equations, we discuss continuous and discrete orthogonal polynomials and explain their connection. 相似文献
17.
In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method. 相似文献
18.
This paper aims to construct a general formulation for the Jacobi operational matrix of fractional integral operator. Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. Therefore, a reliable and efficient technique for the solution of them is too important. For the concept of fractional derivative we will adopt Caputo’s definition by using Riemann–Liouville fractional integral operator. Our main aim is to generalize the Jacobi integral operational matrix to the fractional calculus. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations. The method is applied to solve linear and nonlinear fractional differential equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. 相似文献
19.
We give a new proof of a theorem of Shub and Smale on the expectation of the number of roots of a system of m random
polynomial equations in m real variables, having a special isotropic Gaussian distribution. Further, we present a certain number
of extensions, including the behavior as m → +∞ of the variance of the number of roots, when the system of equations is also stationary. 相似文献
20.
《Journal of Computational and Applied Mathematics》2005,173(2):295-302
Systems of algebraic equations with interval coefficients are very common in several areas of engineering sciences. The computation of the solution of such systems is a central problem when the characterization of the variables related by such systems is desired.In this paper we characterize the solution of systems of algebraic equations with real interval coefficients. The characterization is obtained considering the approach introduced in J. Comput. Appl. Math. 136 (2001) 271. 相似文献